Journal of Mathematical Fluid Mechanics

, Volume 2, Issue 1, pp 16–98

On the Strong Solvability of the Navier—Stokes Equations

  • H. Amann

DOI: 10.1007/s000210050018

Cite this article as:
Amann, H. J. math. fluid mech. (2000) 2: 16. doi:10.1007/s000210050018


In this paper we study the strong solvability of the Navier—Stokes equations for rough initial data. We prove that there exists essentially only one maximal strong solution and that various concepts of generalized solutions coincide. We also apply our results to Leray—Hopf weak solutions to get improvements over some known uniqueness and smoothness theorems. We deal with rather general domains including, in particular, those having compact boundaries.

Keywords. Weak, very weak, and strong solutions; existence and uniqueness theorems with rough initial data. 

Copyright information

© Birkhäuser Verlag, Basel, 2000

Authors and Affiliations

  • H. Amann
    • 1
  1. 1.Institut für Mathematik, Universität Zürich, Winterthurerstr. 190, CH-8057 Zürich, SwitzerlandFR

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